Causes of ethnic segregation in a nineteenth century city

The case of Vyborg

Antti Härkönen

UEF

2024-09-26

Introduction

Vyborg, a Karelian city

Map

Vyborg, a Karelian city

  • castle founded in the late 13th century
  • town privileges 1403

Sources

Poll tax records

poll tax record columns in 1894
column description
plot_number Plot number
taxpayer_men Men paying poll tax
taxpayer_women Women paying poll tax
no_tax_men Men exempt from poll tax
no_tax_women Women exempt from poll tax
in_russia_men Men legally residing in Russia proper
in_russia_women Women legally residing in Russia proper
total_men Total men
total_women Total women
independent Civil servants, entrepreneurs, and financially independent
white_collar White collar workers
worker_industry Workers in industry
worker_other Other workers
servants Servants
other Other employment status
non_resident Resident elsewhere
orthodox Orthodox
other_christian Non-Lutheran and non-Orthodox Christian
other_religion Other religions
draftable 21-year-old males eligible for draft

Estimating the size of Russian population

  • over 90% of Orthodox in Vyborg Russian

Estimating the size of Lutheran population

\[ \begin{equation} P_{Lutheran} = \begin{split} (P_{total\_men}+P_{total\_women}) \\ − (P_{Orthodox}+P_{other\_Christian}+P_{other\_religion}) \end{split} \end{equation} \]

Digitized sources

Sources from the National archives of Finland
Signum Original year Digitization process
Town plan of Vyborg. Vyborg military engineer detachment’s archive of plans for fortifications and buildings, 7, 11. 1878 Georeferenced using ground control points, vectorized manually into shapefile
Vyborg province poll tax registers 1880 Digitized manually into CSV
Financial office of the city of Vyborg, Municipal tax levies and payment registers 1880 Digitized manually into CSV

Growth of Vyborg

Map of Vyborg in 1839

Population growth

Population growth in key areas
District 1822 1880
Centre 1192 2506
St. Anna 244 117
Vyborg suburb 642 756
St Petersburg suburb 1512 2685

Spatial analyses

Work flow

Flow chart of workflow

Population surface model

Population surface model

Based on Martin, Tate, and Langford (2000).

\[ P_i=\sum^N_{j=1} P_j w_{ij} \]

\[ w_{ij} = \begin{cases} \left( \frac{k^2 - d^2_{ij}}{k^2 + d^2_{ij}} \right)^\alpha & \text{if} \hspace{1cm} d_{ij < k} \\ 0 & \text{else} \end{cases} \]

Biweight kernel

::: {#cell-kernel profile .cell execution_count=2}

Kernel function

:::

:::

Segregation

1700s

Map Vyborg plot owners in 1768

Map of density of Orthodox population

Map of income distribution in Vyborg

Explaining segregation

Regression model (1)

\[ O_i \sim MvNormal(\mu, \textbf{K}) \]

\[ \mu_i = \beta_{0,k[i]} + \beta_{1,k[i]} \textit{ln(W)} + \beta_{2,k[i]} C_i \]

\[ k \in 1,2,3,4 \hspace{1cm} i,j \in 1,2,3, \dots 539 \]

\[ \beta_k \sim MvNormal \left( \theta, \begin{bmatrix} 0.1 & 0 & 0 \\ 0 & 0.1 & 0 \\ 0 & 0 & 0.1 \end{bmatrix}\right) \]

\[ \theta \sim MvNormal \left( \begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}, \begin{bmatrix} 0.1 & 0 & 0 \\ 0 & 0.1 & 0 \\ 0 & 0 & 0.1 \end{bmatrix}\right) \]

Regression model (2)

\[ \textbf{K}_{ij} = \eta^2 exp(-75 \rho^2 d^2_{ij}) + 0.01 \times I_{540} \]

\[ \eta^2 \sim Normal(1, 0.2) \] \[ \rho^2 \sim Normal(1, 0.2) \]

Multilevel Bayesian regression

Variable Shape Description
O 540 Normalized proportion of Russian Orthodox of the local population
W 540 Smoothed total income in a location in öre
C 540 Distance to nearest Orthodox church in 1799 in kilometres
d 540 x 540 Distance matrix holding pairwise distances between plots
θ 3 Hyperparameter for β
β 4 x 3 Linear regression coefficients for each district
η2 1 Parameter for the covariance function
ρ2 1 Parameter for the covariance function

Plate diagram of Bayesian regression model

Results

Variable Mean SD HDI, 95%
θ0 −0.027 0.096 −0.227 0.15
θ1 0.027 0.085 −0.142 0.193
θ2 −0.135 0.096 −0.309 0.067
β0,0 −0.609 0.299 −1.162 −0.013
β0,1 0.104 0.056 −0.009 0.209
β0,2 −1.076 0.314 −1.702 −0.487
β1,0 0.097 0.3 −0.46 0.743
β1,1 0.142 0.14 −0.117 0.433
β1,2 −0.037 0.316 −0.625 0.626
β2,0 0.118 0.299 −0.509 0.677
β2,1 0.119 0.074 −0.024 0.261
β2,2 −0.287 0.312 −0.905 0.306
β3,0 0.016 0.272 −0.54 0.515
β3,1 0 0.069 −0.141 0.135
β3,2 −0.496 0.248 −0.991 −0.024
scaled η² 0.93 0.04 0.852 1.006
ρ² 1.0 0.099 0.812 1.194

Change of segregation

Spline model (1)

\[ S_i \sim Normal(\mu_i, \sigma) \]

\[ \mu_i = \alpha + \sum_{k=1}^K w_k B_{k,i} \]

\[ \alpha \sim Normal(0.45, 0.01) \] \[ \sigma \sim HalfNormal(0.05) \]

Spline model (2)

\[ B = \begin{bmatrix} 1 & 0.687 & 0.295 & 0.02 & 0 & 0 & 0 & 0 \\ 0 & 0.299 & 0.601 & 0.612 & 0.367 & 0.276 & 0.007 & 0 \\ 0 & 0.015 & 0.104 & 0.367 & 0.612 & 0.658 & 0.209 & 0 \\ 0 & 0 & 0 & 0 & 0.02 & 0.066 & 0.784 & 1 \end{bmatrix} \]

\[ w_k \sim Normal(0, 0.1) \]

Spline model code

import pymc as pm

with pm.Model() as model:
    a = pm.Normal("α", μ_a, σ_a)
    w = pm.Normal("w", mu=μ_w, sigma=σ_w, shape=B.shape[1])
    μ = pm.Deterministic(
      "μ", a + pm.math.dot(np.asarray(B, order="F"), w.T
    ))
    σ = pm.HalfNormal('σ', σ_σ)
    S = pm.Normal("S", μ, σ, observed=regression_data['200'])
    idata = pm.sample(1000, tune=1000, chains=2)

Plate diagram of Bayesian spline regression model

References

Martin, David, Nicholas J. Tate, and Mitchel Langford. 2000. “Refining Population Surface Models: Experiments with Northern Ireland Census Data.” Transactions in GIS 4 (4): 343–60. https://doi.org/https://doi.org/10.1111/1467-9671.00060.